Definite Integral – rational function in absolute value inside ln function on symmetric interval – Exercise 6442

Exercise

Evaluate the integral

$$\int_{-\frac{1}{2}}^{\frac{1}{2}} \ln|\frac{1-x}{1+x}| dx$$

$$\int_{-\frac{1}{2}}^{\frac{1}{2}} \ln|\frac{1-x}{1+x}| dx=0$$